Finding pH

I'm being asked to find the pH of a 0.050 M solution of NaCN.
I figured out the expression to be x^2/ 0.050 -x, now all i need is a value for k, however I'm not given that value. I know the pH depends on the molarity of the hydrogen ion at equilibrium, however to find that I need to find x, and in order to find x I need a value for k. I would appreciate any help, thanks.

He is talking about the equilibrium constant equation.
Btw, i just finished coding a little simple program on finding the equilibrium constant.
Just saves a few keystroked on the annoying calculator :) .

Staff: Mentor

I'm being asked to find the pH of a 0.050 M solution of NaCN.
I figured out the expression to be x^2/ 0.050 -x, now all i need is a value for k, however I'm not given that value. I know the pH depends on the molarity of the hydrogen ion at equilibrium, however to find that I need to find x, and in order to find x I need a value for k. I would appreciate any help, thanks.

I didn't check my book very well, and so later I found a chart that had the Kb value, so I could just used that to divide 10^-14 to find Ka, since Kb x Ka = Kw (10^-14). Once that's done I could have just used that value, plug it into the equation, solve for x, if it passes the 5% test then take the -log of x and had the pH.

There is a very good chance that all of this is wrong. I am basically just trying this problem out for myself as a challenge, for I don't know what pKa is either. I'm guessing...

[tex]pKa = - log Ka[/tex]

[tex]9.31 = - log Ka[/tex]

[tex]10^{-9.31} = Ka[/tex]

[tex]Ka = 4.9*10^{-10}[/tex]

[tex]4.9*10^{-10} = \frac{x^{2}}{.050 - x}[/tex]

[tex]x^{2} + 4.9*10^{-10}x - 2.5*10^{-11}[/tex]

[tex]x = 5.0*10^{-6}[/tex]

[tex]5.0*10^{-6} = [HCN] = [H^{+}][/tex]

[tex]pH = - log (5.0*10^{-6})[/tex]

[tex]pH = 5.30[/tex]

Once again, I know that I am most likely wrong. I assumed that pKa = - log Ka. I also assumed that [HCN] = [H+]. I haven't learned about that yet; we just started acids and bases earlier this week in my class.

I'm interested to see how this problem is really meant to be worked out .